A natural representation of the structures in CPDs is via tree-CPDs [1]}, as illustrated in Figure REF . For all assignments to the parents of a variable \( A \) , a unique leaf in the tree specifies a (conditional) distribution over \( A \) . The path to each leaf dictates the contexts, i.e., partially assigned parents, given which this distribution is used. We can easily represent tree-CPDs using DCs, where each path from the root to a leaf in each tree-CPD maps to a rule.
